Question: Sean adds up all the even integers from 2 to 500, inclusive. Julie adds up all the integers from 1 to 250, inclusive. What is Sean's sum divided by Julie's sum?
Answer: Note that if we factor out a 2, then Sean's sum is $2 + 4 + \cdots + 500 = 2(1 + 2 + \cdots + 250)$. Julie's sum is $1 + 2 + \cdots + 250$. So Sean's sum divided by Julie's sum is $$
\frac{2(1 + 2 + \cdots + 250)}{(1 + 2 + \cdots + 250)} = \boxed{2}.
$$